Neural Network Classification

Overview

In this exercise, the cluster to which a mask is assigned to is predicted using a NNET approach. Here are the steps:

1. create/load random masks (here we load pre-created random masks)
2. split into train and test
3. train
4. test

Load Noisy Data with Clusters

if(!grepl(pattern = 'maskPrj$', getwd())) setwd('maskPrj')
if(!exists('maskData')) load('NoisyData10-6Cluster.rda')
str(maskData)

Split into train and test

Only the train index is randomly generated:

set.seed(123)
trIdx <- sample.int(dim(maskData$x)[1], .80*dim(maskData$x)[1])

Train a NNET Model

Data is loaded and clusters are encoded into the one-hot format:

# Load the keras library
library(keras)
C_train <- to_categorical(maskData$class[trIdx]-1)
C_test <- to_categorical(maskData$class[-trIdx]-1)

A model is defined with the number of output classes, and the number of inputs, and one hidden layer that is twice the size of the input. The size of the hidden layer and the number of hidden layers can be changed to find an optimal setting, a process that could be very time comsuming:

levels(factor(maskData$class))

[1] "1" "2" "3" "4" "5" "6"

k = 6
# Build a sequential model with 361 inputs, 712 hidden neurons and k outputs
model <- keras_model_sequential() %>%
  layer_dense(units = 722, activation = "relu", input_shape = c(361)) %>%
  layer_dense(units = k, activation = "softmax")

# Compile the model with categorical crossentropy loss and adam optimizer
model %>% compile(
  loss = "categorical_crossentropy", # -1/N Sum_i{1 tp N}(Sum_j{1:C}(y_ij * log(p_ij))):
  # y_ij is one-hot coding of the class label; p_ij is the association to class j
  optimizer = "adam",
  metrics = c("accuracy")
)

Now the actual training is performed:

# Train the model for 100 epochs with batch size of 32
history <- model %>% fit(
  x = as.matrix(maskData$x[trIdx,]),
  y = C_train,
  epochs = 20,
  batch_size = 32, #default value
  validation_split = 0.2
)

Epoch 1/20

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18484/18484 [==============================] - 18s 971us/step - loss: 0.1492 - accuracy: 0.9531

18484/18484 [==============================] - 21s 1ms/step - loss: 0.1492 - accuracy: 0.9531 - val_loss: 0.0792 - val_accuracy: 0.9668
Epoch 2/20

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18484/18484 [==============================] - 19s 1ms/step - loss: 0.0864 - accuracy: 0.9647

18484/18484 [==============================] - 22s 1ms/step - loss: 0.0864 - accuracy: 0.9647 - val_loss: 0.0912 - val_accuracy: 0.9623
Epoch 3/20

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18484/18484 [==============================] - 17s 943us/step - loss: 0.0838 - accuracy: 0.9656

18484/18484 [==============================] - 20s 1ms/step - loss: 0.0838 - accuracy: 0.9656 - val_loss: 0.0681 - val_accuracy: 0.9717
Epoch 4/20

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18484/18484 [==============================] - 20s 1ms/step - loss: 0.0819 - accuracy: 0.9669 - val_loss: 0.0694 - val_accuracy: 0.9716
Epoch 5/20

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18484/18484 [==============================] - 19s 1ms/step - loss: 0.0806 - accuracy: 0.9675

18484/18484 [==============================] - 21s 1ms/step - loss: 0.0806 - accuracy: 0.9675 - val_loss: 0.1256 - val_accuracy: 0.9582
Epoch 6/20

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18484/18484 [==============================] - 19s 1ms/step - loss: 0.0794 - accuracy: 0.9680 - val_loss: 0.0817 - val_accuracy: 0.9672
Epoch 7/20

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18484/18484 [==============================] - 16s 885us/step - loss: 0.0791 - accuracy: 0.9682

18484/18484 [==============================] - 19s 1ms/step - loss: 0.0791 - accuracy: 0.9682 - val_loss: 0.0668 - val_accuracy: 0.9723
Epoch 8/20

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18484/18484 [==============================] - 17s 930us/step - loss: 0.0782 - accuracy: 0.9685

18484/18484 [==============================] - 19s 1ms/step - loss: 0.0782 - accuracy: 0.9685 - val_loss: 0.0751 - val_accuracy: 0.9688
Epoch 9/20

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18484/18484 [==============================] - 19s 1ms/step - loss: 0.0781 - accuracy: 0.9684 - val_loss: 0.0837 - val_accuracy: 0.9680
Epoch 10/20

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18484/18484 [==============================] - 16s 870us/step - loss: 0.0781 - accuracy: 0.9686

18484/18484 [==============================] - 18s 989us/step - loss: 0.0781 - accuracy: 0.9686 - val_loss: 0.0913 - val_accuracy: 0.9627
Epoch 11/20

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18484/18484 [==============================] - 18s 949us/step - loss: 0.0779 - accuracy: 0.9687

18484/18484 [==============================] - 20s 1ms/step - loss: 0.0779 - accuracy: 0.9687 - val_loss: 0.0633 - val_accuracy: 0.9738
Epoch 12/20

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18484/18484 [==============================] - 19s 1ms/step - loss: 0.0781 - accuracy: 0.9687 - val_loss: 0.0852 - val_accuracy: 0.9666
Epoch 13/20

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18484/18484 [==============================] - 16s 885us/step - loss: 0.0770 - accuracy: 0.9692

18484/18484 [==============================] - 19s 1ms/step - loss: 0.0770 - accuracy: 0.9692 - val_loss: 0.0820 - val_accuracy: 0.9677
Epoch 14/20

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18484/18484 [==============================] - 16s 877us/step - loss: 0.0777 - accuracy: 0.9691

18484/18484 [==============================] - 18s 997us/step - loss: 0.0777 - accuracy: 0.9691 - val_loss: 0.0685 - val_accuracy: 0.9722
Epoch 15/20

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18484/18484 [==============================] - 17s 919us/step - loss: 0.0770 - accuracy: 0.9693

18484/18484 [==============================] - 19s 1ms/step - loss: 0.0770 - accuracy: 0.9693 - val_loss: 0.0707 - val_accuracy: 0.9711
Epoch 16/20

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18484/18484 [==============================] - 19s 1ms/step - loss: 0.0773 - accuracy: 0.9692

18484/18484 [==============================] - 21s 1ms/step - loss: 0.0773 - accuracy: 0.9692 - val_loss: 0.0609 - val_accuracy: 0.9746
Epoch 17/20

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18484/18484 [==============================] - 21s 1ms/step - loss: 0.0769 - accuracy: 0.9693 - val_loss: 0.1053 - val_accuracy: 0.9625
Epoch 18/20

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18484/18484 [==============================] - 18s 952us/step - loss: 0.0764 - accuracy: 0.9695

18484/18484 [==============================] - 20s 1ms/step - loss: 0.0764 - accuracy: 0.9695 - val_loss: 0.0852 - val_accuracy: 0.9653
Epoch 19/20

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18484/18484 [==============================] - 17s 917us/step - loss: 0.0765 - accuracy: 0.9695

18484/18484 [==============================] - 19s 1ms/step - loss: 0.0765 - accuracy: 0.9695 - val_loss: 0.1285 - val_accuracy: 0.9565
Epoch 20/20

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18088/18484 [============================>.] - ETA: 0s - loss: 0.0757 - accuracy: 0.9697
18145/18484 [============================>.] - ETA: 0s - loss: 0.0757 - accuracy: 0.9697
18201/18484 [============================>.] - ETA: 0s - loss: 0.0757 - accuracy: 0.9697
18257/18484 [============================>.] - ETA: 0s - loss: 0.0757 - accuracy: 0.9697
18315/18484 [============================>.] - ETA: 0s - loss: 0.0757 - accuracy: 0.9697
18372/18484 [============================>.] - ETA: 0s - loss: 0.0757 - accuracy: 0.9697
18428/18484 [============================>.] - ETA: 0s - loss: 0.0758 - accuracy: 0.9697
18484/18484 [==============================] - 17s 920us/step - loss: 0.0758 - accuracy: 0.9697

18484/18484 [==============================] - 19s 1ms/step - loss: 0.0758 - accuracy: 0.9697 - val_loss: 0.0827 - val_accuracy: 0.9691

Test the Model

The performance of the model is measured on the test data:

model %>% evaluate(maskData$x[-trIdx,], C_test) -> nnetAccur

   1/5776 [..............................] - ETA: 1:25 - loss: 0.0862 - accuracy: 0.9375
 109/5776 [..............................] - ETA: 2s - loss: 0.0304 - accuracy: 0.9880  
 221/5776 [>.............................] - ETA: 2s - loss: 0.0469 - accuracy: 0.9785
 333/5776 [>.............................] - ETA: 2s - loss: 0.0692 - accuracy: 0.9700
 447/5776 [=>............................] - ETA: 2s - loss: 0.0686 - accuracy: 0.9709
 561/5776 [=>............................] - ETA: 2s - loss: 0.0774 - accuracy: 0.9698
 672/5776 [==>...........................] - ETA: 2s - loss: 0.0723 - accuracy: 0.9721
 784/5776 [===>..........................] - ETA: 2s - loss: 0.0695 - accuracy: 0.9726
 895/5776 [===>..........................] - ETA: 2s - loss: 0.0794 - accuracy: 0.9690
1007/5776 [====>.........................] - ETA: 2s - loss: 0.0784 - accuracy: 0.9691
1119/5776 [====>.........................] - ETA: 2s - loss: 0.0817 - accuracy: 0.9690
1233/5776 [=====>........................] - ETA: 2s - loss: 0.0795 - accuracy: 0.9702
1342/5776 [=====>........................] - ETA: 1s - loss: 0.0766 - accuracy: 0.9710
1452/5776 [======>.......................] - ETA: 1s - loss: 0.0800 - accuracy: 0.9692
1562/5776 [=======>......................] - ETA: 1s - loss: 0.0803 - accuracy: 0.9691
1672/5776 [=======>......................] - ETA: 1s - loss: 0.0822 - accuracy: 0.9688
1777/5776 [========>.....................] - ETA: 1s - loss: 0.0818 - accuracy: 0.9695
1873/5776 [========>.....................] - ETA: 1s - loss: 0.0796 - accuracy: 0.9702
1987/5776 [=========>....................] - ETA: 1s - loss: 0.0814 - accuracy: 0.9693
2099/5776 [=========>....................] - ETA: 1s - loss: 0.0828 - accuracy: 0.9686
2212/5776 [==========>...................] - ETA: 1s - loss: 0.0820 - accuracy: 0.9689
2324/5776 [===========>..................] - ETA: 1s - loss: 0.0831 - accuracy: 0.9689
2436/5776 [===========>..................] - ETA: 1s - loss: 0.0806 - accuracy: 0.9698
2549/5776 [============>.................] - ETA: 1s - loss: 0.0805 - accuracy: 0.9696
2662/5776 [============>.................] - ETA: 1s - loss: 0.0824 - accuracy: 0.9686
2713/5776 [=============>................] - ETA: 1s - loss: 0.0820 - accuracy: 0.9688
2730/5776 [=============>................] - ETA: 1s - loss: 0.0817 - accuracy: 0.9688
2826/5776 [=============>................] - ETA: 1s - loss: 0.0817 - accuracy: 0.9690
2939/5776 [==============>...............] - ETA: 1s - loss: 0.0812 - accuracy: 0.9694
3052/5776 [==============>...............] - ETA: 1s - loss: 0.0796 - accuracy: 0.9699
3167/5776 [===============>..............] - ETA: 1s - loss: 0.0809 - accuracy: 0.9692
3280/5776 [================>.............] - ETA: 1s - loss: 0.0812 - accuracy: 0.9691
3396/5776 [================>.............] - ETA: 1s - loss: 0.0816 - accuracy: 0.9692
3509/5776 [=================>............] - ETA: 1s - loss: 0.0816 - accuracy: 0.9694
3616/5776 [=================>............] - ETA: 1s - loss: 0.0805 - accuracy: 0.9698
3731/5776 [==================>...........] - ETA: 0s - loss: 0.0812 - accuracy: 0.9694
3844/5776 [==================>...........] - ETA: 0s - loss: 0.0816 - accuracy: 0.9691
3960/5776 [===================>..........] - ETA: 0s - loss: 0.0815 - accuracy: 0.9692
4074/5776 [====================>.........] - ETA: 0s - loss: 0.0816 - accuracy: 0.9693
4186/5776 [====================>.........] - ETA: 0s - loss: 0.0804 - accuracy: 0.9697
4299/5776 [=====================>........] - ETA: 0s - loss: 0.0815 - accuracy: 0.9691
4412/5776 [=====================>........] - ETA: 0s - loss: 0.0819 - accuracy: 0.9688
4523/5776 [======================>.......] - ETA: 0s - loss: 0.0817 - accuracy: 0.9689
4639/5776 [=======================>......] - ETA: 0s - loss: 0.0827 - accuracy: 0.9689
4751/5776 [=======================>......] - ETA: 0s - loss: 0.0815 - accuracy: 0.9692
4864/5776 [========================>.....] - ETA: 0s - loss: 0.0817 - accuracy: 0.9690
4978/5776 [========================>.....] - ETA: 0s - loss: 0.0824 - accuracy: 0.9688
5091/5776 [=========================>....] - ETA: 0s - loss: 0.0821 - accuracy: 0.9689
5205/5776 [==========================>...] - ETA: 0s - loss: 0.0827 - accuracy: 0.9688
5315/5776 [==========================>...] - ETA: 0s - loss: 0.0817 - accuracy: 0.9692
5428/5776 [===========================>..] - ETA: 0s - loss: 0.0816 - accuracy: 0.9692
5541/5776 [===========================>..] - ETA: 0s - loss: 0.0823 - accuracy: 0.9688
5654/5776 [============================>.] - ETA: 0s - loss: 0.0821 - accuracy: 0.9689
5768/5776 [============================>.] - ETA: 0s - loss: 0.0829 - accuracy: 0.9688
5776/5776 [==============================] - 3s 462us/step - loss: 0.0829 - accuracy: 0.9688

5776/5776 [==============================] - 3s 463us/step - loss: 0.0829 - accuracy: 0.9688

nnetAccur

      loss   accuracy 
0.08293779 0.96882576